A model of chiasma reduction is developed, evaluated by computer simulation and discussed in relation to the evolution of interference. The model assumes that adjacently formed crossovers can interact, if there is incomplete sister chromatid cohesion between them, and give rise to a reduced number of chiasmata. In the absence of crossover position interference this leads to a considerable risk of non-disjunction for an average sized chromosome. It is suggested that an important function of crossover interference is to reduce this effect. The question is raised whether chiasma reduction takes place today. Some available cytological data can be interpreted as showing that chiasma reduction occurs in normal meiosis. The possibility of chiasma reduction therefore needs further attention.